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Computability Theory and Foundations of Mathematics cover

This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.

Sample Chapter(s)
Preface
Chi-Tat Chong's Work on Reverse Mathematics

Contents:

  • Chi-Tat Chong's Work on Reverse Mathematics (Yue Yang)
  • On One-Variable Fragments of Modal µ-Calculus (Leonardo Pacheco, Wenjuan Li and Kazuyuki Tanaka)
  • Infinite Games, Inductive Definitions and Transfinite Recursion (Kazuyuki Tanaka and Keisuke Yoshii)
  • A Survey of the Distributional Complexity for AND-OR Trees (Weiguang Peng)
  • Rational Sequences Converging to Left-c.e. Reals of Positive Effective Hausdorff Dimension (Hiroyuki Imai, Masahiro Kumabe, Kenshi Miyabe, Yuki Mizusawa and Toshio Suzuki)
  • Takeuti-Yasumoto Forcing Revisited (Satoru Kuroda)
  • Permission and Obligation in Ceteris Paribus (Huimin Dong)
  • Reverse Mathematics of Separation Theorems in Lattice Theory (Junren Ru and Guohua Wu)

Readership: Researchers in mathematical logic and foundation, and theoretical computer science.

Free Access
FRONT MATTER
  • Pages:i–xvi

https://doi.org/10.1142/9789811259296_fmatter

Free Access
Chi-Tat Chong’s Work on Reverse Mathematics
  • Pages:1–15

https://doi.org/10.1142/9789811259296_0001

No Access
On One-Variable Fragments of Modal µ-Calculus
  • Pages:17–45

https://doi.org/10.1142/9789811259296_0002

No Access
Infinite Games, Inductive Definitions and Transfinite Recursion
  • Pages:47–78

https://doi.org/10.1142/9789811259296_0003

No Access
A Survey of the Distributional Complexity for AND-OR Trees
  • Pages:79–96

https://doi.org/10.1142/9789811259296_0004

No Access
Rational Sequences Converging to Left-c.e. Reals of Positive Effective Hausdorff Dimension
  • Pages:97–121

https://doi.org/10.1142/9789811259296_0005

No Access
Takeuti-Yasumoto Forcing Revisited
  • Pages:123–155

https://doi.org/10.1142/9789811259296_0006

No Access
Permission and Obligation in Ceteris Paribus
  • Pages:157–165

https://doi.org/10.1142/9789811259296_0007

No Access
Reverse Mathematics of Separation Theorems in Lattice Theory
  • Pages:167–177

https://doi.org/10.1142/9789811259296_0008